Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Lieb-Thirring inequality revisited

Rupert L. Frank, Dirk Hundertmark, Michal Jex, Phan Thành Nam

Abstract

We provide new estimates on the best constant of the Lieb-Thirring inequality for the sum of the negative eigenvalues of Schrödinger operators, which significantly improve the so far existing bounds.

The Lieb-Thirring inequality revisited

Abstract

We provide new estimates on the best constant of the Lieb-Thirring inequality for the sum of the negative eigenvalues of Schrödinger operators, which significantly improve the so far existing bounds.

Paper Structure

This paper contains 6 sections, 11 theorems, 96 equations.

Table of Contents

  1. Introduction
  2. Optimal momentum decomposition
  3. Lifting to higher dimensions. I
  4. Low momentum averaging
  5. Lifting to higher dimensions. II
  6. Bounds with fractional operators

Key Result

Theorem 1

For all $d\ge 1$, the best constant in the Lieb--Thirring inequality eq:LT-sum-eigenvalue satisfies

Theorems & Definitions (20)

  • Theorem 1
  • Theorem 2
  • Corollary 3
  • Proposition 4
  • proof
  • Lemma 5
  • proof
  • Proposition 6
  • proof
  • Remark 7
  • ...and 10 more